Optimal approach to quantum communication using dynamic programming

Abstract

Reliable preparation of entanglement between distant systems is an outstanding problem in quantum information science and quantum communication. In practice, this has to be accomplished by noisy channels (such as optical fibers) that generally result in exponential attenuation of quantum signals at large distances. A special class of quantum error correction protocols, quantum repeater protocols, can be used to overcome such losses. In this work, we introduce a method for systematically optimizing existing protocols and developing more efficient protocols. Our approach makes use of a dynamic programmingbased searching algorithm, the complexity of which scales only polynomially with the communication distance, letting us efficiently determine near-optimal solutions. We find significant improvements in both the speed and the final-state fidelity for preparing long-distance entangled states.entanglement ͉ optimal control ͉ quantum information ͉ quantum repeater S equential decision-making in probabilistic systems is a widely studied subject in the field of economics, management science, and engineering. Applications range from problems in scheduling and asset management to control and estimation of dynamical systems (1). In this article we use these techniques for solving a class of decision-making problems that arise in quantum information science (2, 3). Specifically we consider the optimal design of a so-called quantum repeater for quantum communication. Such repeaters have potential application in quantum communication protocols for cryptography (4-6) and information processing (7), where entangled quantum systems located at distant locations are used as a fundamental resource. In principle, this entanglement can be generated by sending a pair of entangled photons through optical fibers. However, in the presence of attenuation, the probability of success in preparing a distant entangled pair decreases exponentially with distance (8).Quantum repeaters can reduce such exponential scaling to polynomial scaling with distance and thus provide an avenue to long-distance quantum communication even with fiber attenuation. The underlying idea of quantum repeater (9, 10) is to generate a backbone of entangled pairs over much shorter distances, store them in a set of distributed nodes, and perform a sequence of quantum operations with only a finite probability of success. Purification operations (11, 12) improve the fidelity of the entanglement in the backbone, and connection operations join two shorter-distance entangled pairs of the backbone to form a single, longer-distance entangled pair. By relying on a quantum memory at each node to let different sections of the repeater reattempt failed operations independently, a high-fidelity entangled state between two remote quantum systems can be produced in polynomial time. A quantum repeater protocol is a set of rules that determine the choice and ordering of operations based on previous results. An optimal protocol is one that produces entangled pairs of a desired fidelity ...

Quantum repeaters based on atomic ensembles and linear optics

“…There are also numerous contributions to the field of quantum repeaters that take a longer-term and/or more abstract view. Examples include work on the use of dynamic programming (Jiang et al, 2007a), error correcting codes (Jiang et al, 2008), decoherence-free subspaces (Dorner et al, 2008), and an analysis of the role of memory errors (Hartmann et al, 2007).…”

Ultrafast and Fault-Tolerant Quantum Communication across Long Distances

“…The first class of QRs [6][7][8][9] reduces the exponential scaling of fiber loss to polynomial scaling by introducing intermediate QR nodes. However, this scheme for long distance quantum communication is relatively slow [13], even after optimization [14], limited by the time associated with two-way classical communication between remote stations required for the entanglement purification process needed to correct operational errors [15]. In contrast, the second class of QRs introduce quantum encoding and classical error correction to replace the entanglement purification with classical error correction, handling all operational errors [10,16].…”

Control of Photon Storage Time in Photon Echoes using a Deshelving Process

“…This distance should limit applications of quantum information especially for long-distance quantum communications. To solve the limited photon transmission, a quantum repeater has been introduced for virtually unlimited transmission distance (Duan et al, 2001;Jiang et al, 2007;Simon et al, 2007;Waks et al, 2002). Quantum memory is an essential element for the entangled photon swapping in the quantum repeaters.…”